Magnetic field line random walk and solar energetic particle path lengths

Stochastic theory and PSP/IS⊙IS observations

¹ Department of Physics and Astronomy and Bartol Research Institute, University of Delaware, Newark, DE 19716, USA
e-mail: rohitc@udel.edu
² Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt MD 20771, USA
e-mail: rohit.chhiber@nasa.gov
³ California Institute of Technology, Pasadena, CA 91125, USA
⁴ Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
⁵ Faculty of Engineering and Technology, Panyapiwat Institute of Management, Nonthaburi 11120, Thailand
⁶ Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
⁷ National Astronomical Research Institute of Thailand (NARIT), Chiang Mai 50180, Thailand
⁸ 33/5 Moo 16, Tambon Bandu, Muang District, Chiang Rai 57100, Thailand
⁹ Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
¹⁰ University of Maryland Baltimore County, Baltimore, MD 21250, USA
¹¹ University of Arizona, Tucson, AZ 85721, USA
¹² University of New Hampshire, Durham, NH, 03824, USA
¹³ Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA
¹⁴ University of Texas at San Antonio, San Antonio, TX 78249, USA
¹⁵ Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Received: 30 October 2020
Accepted: 17 January 2021

Abstract

Context. In 2020 May-June, six solar energetic ion events were observed by the Parker Solar Probe/IS⊙IS instrument suite at ≈0.35 AU from the Sun. From standard velocity-dispersion analysis, the apparent ion path length is ≈0.625 AU at the onset of each event.

Aims. We develop a formalism for estimating the path length of random-walking magnetic field lines to explain why the apparent ion path length at an event onset greatly exceeds the radial distance from the Sun for these events.

Methods. We developed analytical estimates of the average increase in path length of random-walking magnetic field lines, relative to the unperturbed mean field. Monte Carlo simulations of field line and particle trajectories in a model of solar wind turbulence were used to validate the formalism and study the path lengths of particle guiding-center and full-orbital trajectories. The formalism was implemented in a global solar wind model, and the results are compared with ion path lengths inferred from IS⊙IS observations.

Results. Both a simple estimate and a rigorous theoretical formulation are obtained for field-lines’ path length increase as a function of path length along the large-scale field. From simulated field line and particle trajectories, we find that particle guiding centers can have path lengths somewhat shorter than the average field line path length, while particle orbits can have substantially longer path lengths due to their gyromotion with a nonzero effective pitch angle.

Conclusions. The long apparent path length during these solar energetic ion events can be explained by (1) a magnetic field line path length increase due to the field line random walk and (2) particle transport about the guiding center with a nonzero effective pitch angle due to pitch angle scattering. Our formalism for computing the magnetic field line path length, accounting for turbulent fluctuations, may be useful for application to solar particle transport in general.